The Dodgers also sent minor league right-handers Blake Johnson and Julio Pimental and cash considerations to the Royals for right-hander Elmer Dessens.
Perez, a former 15-game winner who spent much of the season in the bullpen due to ineffectiveness, accused the Dodgers of treating him like "trash" on July 13 after he gave up a game-winning home run to Albert Pujols in St. Louis.
"I'm mad because I'm leaving this town. My best years have been here," said Perez, who came to the Dodgers with outfielder Brian Jordan in a January 2002 trade that sent Gary Sheffield to the Atlanta Braves. "Sometimes people judge you because they think your work habits haven't been the same. But that's not true. As a professional, you have your ups and downs. But I don't think I have any mechanical problems."
Perez, who pitched two one-hitters in 2002 and made the All-Star team that season for the only time in his career, is in the second year of a three-year, $24 million contract and in his sixth season with the Dodgers. He won 15 games in '02 and 12 in '03, but he was 7-8 in an injury-plagued 2005.
"This year has been tough," Perez said. "But at the same time, I really appreciate what the people in the front office and the fans have done for me since I've been here. I had a great time here. I didn't want to leave, but it's a business. It's time to move on. It's time to go to a different franchise and show I still have the skill to pitch and the stuff to do it."
But when talking with ESPNdeportes.com's Enrique Rojas, Perez had a different take on the situation.
"They treated me like garbage with the things they did to me," he said of the team's front office. Although he did not refer to manager Grady Little or Dodgers general manager Ned Colletti by name, Perez indicated that his place on the team changed when manager Jim Tracy and GM Paul DePodesta left.
"I don't know if some of the new guys in the organization just don't like me or what, but I can say that I really have no respect for them because they didn't have the guts to tell me how things really were. I was always lied to."
Wearing a style of hat made famous by the late actor Jim Hutton in the 1970s TV show "Ellery Queen," Perez entered the Dodgers' clubhouse about three hours before gametime and casually cleaned out his locker with help from his cousin. Perez did have words of praise for Jim Colborn, who was his pitching coach for five seasons in Los Angeles. Colborn accompanied Tracy to Pittsburgh in November after Tracy's five-year stint with the Dodgers ended.
"Jim Colborn was like a father for me and he was a first-class coach," Perez said. "He helped to make me understand the kind of pitcher I was, working with all of my pitches. When you were doing bad, he tried to put you in a mentality that you felt you were good. Just because you had two or three bad starts, it doesn't mean you're bad. I learned a lot of stuff from him and Jim Tracy and the coaches staff that were here before."
Royals general manager Dayton Moore, who came to Kansas City from the Braves' front office, said he has known Perez since he was a young prospect in the Atlanta organization.
"Whatever has happened in the past is very manageable," Moore said. "We feel very, very secure in our belief that he is going to come here and do a good job on the field certainly and off the field as well."
Moore said Perez will be used in the starting rotation once his arm is stretched out again.
"Moving him was something we really needed to do for all concerned, including him," Colletti said on a conference call. "He lost his starting job, obviously. It's probably best to cut ties and move on. We were not getting much productivity out of that roster spot."
Perez appears happy to be headed to Kansas City, telling ESPNdeportes.com that "this is the best thing that could have happened. In Kansas City, I'll have my turn in the rotation, and I should get more consideration."
Colletti said the Royals wouldn't accept a straight-up trade for Perez, and they demanded prospects and cash, too.
"It hasn't been easy," he said. "If it was easy, it would've happened a while ago."
Despite the team's recent public comments, Colletti had been in active discussions about trading Perez.
"I'd rather not say exactly how long, but I'll say quite a while," he said.
The last-place Dodgers have lost 11 of 12 and were 5½ games behind NL West-leading San Diego going into Tuesday night's game at home against the Padres.
Dessens returns for a second stint with the Dodgers, having appeared in 28 games for them last season, including seven starts. He had a 3.56 ERA in 65 2/3 innings.
In 2004, the 35-year-old pitcher was 1-0 with a 3.20 ERA in 12 games following an August trade to the Dodgers from Arizona.
This season, Dessens had a 4.50 ERA in 43 games for the Royals.
Colletti said Dessens will work out of the bullpen and could be an occasional starter.
Information from The Associated Press was used in this report.